Over　the　last　few　decades,　the　use　of　renewable　and　clean　energy　sources　has　been　the　core　of　attention　of　the　researchers.　Besides,　utilization　of　the　energy　hubs　as　a　great　innovation　for　future　multi-carrier　energy　systems　is　well　perceived　for　integrating　intermittent　sources　of　energy　into　the　energy　systems,　which　is　surged　and　bolded　in　recent　years.　In　this　regard,　this　paper　proposes　an　effective　distributed　energy　management　framework　for　modeling　and　optimal　operation　management　of　clean　smart　islands　based　on　primal-dual　method　of　multipliers.　The　primal-dual　method　of　multipliers　approach　has　shown　superior　performance　compared　to　the　alternating　method　of　multipliers　for　distributed　optimization.　In　this　study,　two　different　agents　including　a　smart　energy　hub　and　a　microgrid　comprises　of　renewable　and　clean　energy　sources　are　considered　in　the　smart　island.　These　two　distinct　energy　systems　are　assumed　to　be　equipped　with　communication　apparatuses　and　are　intended　to　negotiate　over　the　energy　they　need　in　a　proper　and　completely　distributed　manner.　Results　show　the　effectiveness,　accuracy　and　applicability　of　the　approach　for　energy　communication.　©　2020　Elsevier　Ltd